Other than ESF, there are plenty of international schools.
Many of them, especially those on the Hong Kong Island and in the Kowloon side (such as the Australian Int'l, French Int'l, German-Swiss Int'l, just to name a few), however, do have long waiting lists. Nevertheless, in the New Territories side a few of them should have rooms, or at least, not have long queues. I particularly recommend Japanese Int'l, which offers high quality primary education (following the IB Primary year programme). (Well, not sure if I have to declare the possible conflict of interest: my kids are studying there.) Then a natural question is: why there are rooms. Well, because of the uneven spatial distribution of wealth! While local schools are free, every Int'l school is charging a handsome amount and only middle-middle class or above would find them affordable, and more middle-middle class families are living on the Island or in Kowloon than in the New Territories, because most of them are working in the Central, Wan Chai and Causeway Bay (Hong Kong Island) or Tsim Sha Tsui, Jordan and Mongkok (Kowloon).
What may seem contradictory to my above argument is that the (only) ESF school in the New Territories, Shatin Junior/Shatin College, has probably the longest waiting list among all ESF school, whilst those in the five primary and three secondary ESF schools on the Island are shorter. However, I believe it is because of the difference in the ratios of the number of places to the population size. I do not have any figures at hand but I remember that the population size of the Island is much much smaller than that in the New Territories.
Anyway, my simple answer is the original question is: NO, not hopeless; you definitely can find a good school for your kids if you do not restrict yourself to a particular one.
